In our search of vortex solutions for this model we are specially interested in the emergence of a hidden scalar condensate at \(r=0\) , triggered by an energy decrease leading to a stable condensate configuration at expenses of the visible scalar energy. This “competing order” phenomenon has been previously discussed in the context of superconducting superstrings [1]}, topological defects [2]}, [3]} and, remarkably, in the context of condensed matter physics concerning the study of high-temperature superconductors [4]}.
